Authors:
- A comprehensive revision of a classic text relating geometic field theory to modern physics
- Offers an up-to-date overview of geometrodynamics including minimal topological models
- Contains new chapters on teleparalelism, Chern-Simons-induced topological 3D gravity and supergravity, quantization via topological ghosts, constrained BF model with SL (5, R) gauge group, and chiral and trace anomalies
- Provides a detailed exposition of frame bundles in gravity
- Includes supplementary material: sn.pub/extras
Part of the book series: Mathematical Physics Studies (MPST)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
About this book
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed.
Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.
Authors and Affiliations
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Departamento de Física, CBI Iztapalapa, Universidad Autónoma Metropolitan, Mexico City, Mexico
Eckehard W. Mielke
About the author
He is the author of the Springer book "Sonne, Mond und .... Schwarze Locher" (1997) (Sun, Moon and...Black Holes), a popular book offering a short trip through recent developments in astronomy.
Bibliographic Information
Book Title: Geometrodynamics of Gauge Fields
Book Subtitle: On the Geometry of Yang-Mills and Gravitational Gauge Theories
Authors: Eckehard W. Mielke
Series Title: Mathematical Physics Studies
DOI: https://doi.org/10.1007/978-3-319-29734-7
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2017
Hardcover ISBN: 978-3-319-29732-3Published: 09 February 2017
Softcover ISBN: 978-3-319-80638-9Published: 12 July 2018
eBook ISBN: 978-3-319-29734-7Published: 22 January 2017
Series ISSN: 0921-3767
Series E-ISSN: 2352-3905
Edition Number: 2
Number of Pages: XVII, 373
Number of Illustrations: 10 b/w illustrations, 8 illustrations in colour
Topics: Classical and Quantum Gravitation, Relativity Theory, Mathematical Physics, Elementary Particles, Quantum Field Theory